An important goal in the exploration and production of hydrocarbons is to determine how much oil or gas, as the case may be, can be made to flow out of a reservoir rock formation via a producing borehole, and at what rates. These crucial parameters depend fundamentally on the permeability of the formation, the existence of fractures, and the viscosity of the fluid. It would be extremely useful to be able to predict what is the permeability of a particular earth formation traversed by a borehole, without going to the extraordinary trouble and expense of some known techniques such as that of artificially injecting fluid into that formation. Such an artificial injection procedure would require that the entire borehole, other than the selected zone of interest, be sealed off from the testing fluid, and this is time consuming and obviously troublesome. Furthermore, such injection tests can be made only for selected formations at a time, and cannot produce a continuous measurement of permeability for all zones of interest traversed by the borehole.
For the above reasons there have been strong incentives within the industry to provide reliable methods for determining formation permeability using an acoustic wireline log or some other continuous measurement which can be made during the drilling process itself, or very shortly thereafter. These various techniques are well known in the industry and will not be discussed herein, with the exception of the acoustic techniques.
The idea of using an acoustic tube wave propagating within the borehole to measure formation permeability was proposed many years ago and was considered to be conceptually promising but practically problematic. The tube wave, also commonly referred to as a Stoneley wave, is a guided surface wave which travels in the direction of the borehole axis. J. E. White has explained in his book, Underground Sound, Elsevier (1983), that a low frequency tube wave in a permeable borehole can be viewed as a pulsating pressure which displaces fluid alternately into and out of the borehole wall. He has set forth, in Chapter 5 of his book, some of the basic mathematical expressions which form one representation of the relationship between formation permeability and the acoustic tube wave velocity.
Actual logging techniques have been proposed which attempt to correlate measured tube wave amplitudes to the permeability of a formation traversed by the tube wave. In "Synthetic Microseismograms: Logging in Porous Formations", Geophysics, Vol. 39, No. 1, (Feb. 1974), J. H. Rosenbaum has computed the waveforms generated by a logging tool using Biot's theory to model the fluid saturated formation. He was able to relate the amplitude of the tube wave to permeability. Rosenbaum noted in this paper that the behavior of the mudcake (typically on the borehole wall surface) is described by the surface mudcake impedance factor Z.sub.m, which is assumed to be equal to infinity in the case of a "sealed interface", and equal to zero in the case of an "open interface".
Others at Shell have reported some correlations between the acoustic energy of the tube wave, as measured by a commercially available Schlumberger acoustic tool, with measured formation permeability. This is reported in J. J. Staal and J. D. Robinson, "Permeability Profiles from Acoustic Logging", SPE Paper 6821, 52nd Annual Fall Technical Conference, Oct. 9-12, 1977, as a qualitative permeability correlation made between rock cores extracted from the borehole on one hand, and acoustic logs on the other. Although this kind of empirical correlation can be made for any one well by imposing certain "best fit" conditions, the correlation is not generally valid for other wells or other reservoirs, and therefore lacks predictive power.
U.S. Pat. No. 4,575,828 to Williams describes a method which attempts to determine both the permeability due to the rock matrix and the permeability due to fractures in the rock, using the ratio of tube wave amplitudes and travel times, respectively, measured at two spaced apart receivers in the borehole. Although this method also obtains results which may correlate with field data in a single well, it is believed that the method cannot consistently predict permeability in multiple wells. In fact, it is believed that none of the methods to date have been successful in quantitatively predicting permeability in boreholes.
Thus, despite the strong interest in linking acoustic waves and permeability, as shown by the above and other studies in this field, the reported eperimental results and field measurements have not heretofor yielded a clear quantitative connection which can reliably predict permeability in oil wells.
Accordingly, it is an object of the present invention to provide an improved method for quantitatively determining formation permeability using measured acoustic tube wave characteristics.
It is also an object of the invention to determine formation permeability with or without the making of comparisons to extracted cores.
It is additionally an object of the invention to impose alternative and more realistic boundary conditions for a mudcake layer in the borehole in the determination of formation permeability.
It is also an object of the invention to modify the conventional methods for determining permeability with a finite mudcake impedance contribution and a mudcake layer contribution due to elastic deformation of a mudcake layer having a finite thickness.